$(( )) reads a number in any base and does checked 64-bit arithmetic

CHANGELOG.md

@@ -15,9 +15,17 @@ breaking entries are marked **BREAKING**.
   an `ExecContext` can spawn a child with the kernel's external-command
   discipline. `tools::DEFAULT_KILL_GRACE` is 2s. Only a struct literal changes.
 
+- **Arithmetic diverges from bash on purpose** — overflow, an unset/empty
+  operand, and a leading zero are errors, never a wrap or 0; strings are
+  values, not expressions; a skipped `&&`/`||`/`?:` branch's `$(...)` never
+  runs.
+
 ### Added
 - **`random` builtin** — `random [--min N] [--max N]` prints one uniformly
   chosen integer, typed; the default range is bash's `$RANDOM` (0 to 32767).
+- **`$(( ))` reads another base** (`0x`, `base#digits`, `base#$var`) and
+  does checked 64-bit arithmetic with the full C operator set through `?:`;
+  `$(...)` is an operand; bare `(( expr ))` is a condition, like `[[ ]]`.
 
 - **Wrapped commands** (`kaish_kernel::tools::wrapped`, `subprocess` feature):
   register an external program as a tool with a declared grammar. Verbs and flags

crates/kaish-help/content/en/syntax.md

@@ -339,12 +339,21 @@ DATA=$(kaish-last)                # capture for later use
 ## Arithmetic
 
 ```sh
-X=$((5 + 3))              # 8
-Y=$((X * 2))              # 16
-# Operators: + - * / % > < >= <= == !=
-# Comparisons return 1/0
+echo $((5 + 3 * 2))       # 11    checked 64-bit integers; overflow is an error
+echo $((0xff))            # 255   hex; also $((16#ff)) — base#digits, base 2 to 36
+echo $((8#17))            # 15    octal; $((010)) is an error — write 8#10 or 10
+m=$(date +%m); echo $((10#$m + 1))   # text with a leading zero, read as decimal
+echo $((2 ** 10))         # 1024
+echo $((5 > 3))           # 1     comparisons return 1 or 0
+echo $((a > b ? a : b))   # ternary; && || ? : skip the side they do not need
+echo $(( $(wc -l < f) * 2 ))         # $(cmd) is an operand
+x=$((x + 1))              # assignment stays outside; x++ is an error
+while (( i <= 5 )); do ...; done     # (( )) alone is a condition
 ```
 
+Operators, highest first: `+ - ! ~` · `**` · `* / %` · `+ -` · `<< >>` · `< <= > >=` · `== !=` · `&` · `^` · `|` · `&&` · `||` · `? :`.
+An unset variable, a float, or `$RANDOM` is an error that names the fix.
+
 ## Functions
 
 ```sh

crates/kaish-help/src/fragments.rs

@@ -645,11 +645,20 @@ DATA=$(kaish-last)                # capture for later use
         "arithmetic",
         "Arithmetic",
         r#"```sh
-X=$((5 + 3))              # 8
-Y=$((X * 2))              # 16
-# Operators: + - * / % > < >= <= == !=
-# Comparisons return 1/0
-```"#,
+echo $((5 + 3 * 2))       # 11    checked 64-bit integers; overflow is an error
+echo $((0xff))            # 255   hex; also $((16#ff)) — base#digits, base 2 to 36
+echo $((8#17))            # 15    octal; $((010)) is an error — write 8#10 or 10
+m=$(date +%m); echo $((10#$m + 1))   # text with a leading zero, read as decimal
+echo $((2 ** 10))         # 1024
+echo $((5 > 3))           # 1     comparisons return 1 or 0
+echo $((a > b ? a : b))   # ternary; && || ? : skip the side they do not need
+echo $(( $(wc -l < f) * 2 ))         # $(cmd) is an operand
+x=$((x + 1))              # assignment stays outside; x++ is an error
+while (( i <= 5 )); do ...; done     # (( )) alone is a condition
+```
+
+Operators, highest first: `+ - ! ~` · `**` · `* / %` · `+ -` · `<< >>` · `< <= > >=` · `== !=` · `&` · `^` · `|` · `&&` · `||` · `? :`.
+An unset variable, a float, or `$RANDOM` is an error that names the fix."#,
     ),
     syntax_section(
         "functions",